Answer : $x^2+8y-32=0$
The coordinates of the vertex is $(0,4)$
The coordinates of the focus is $(0,2)$
It is clear that the vertex and the focus lies on the positive side of the y-axis.
Hence the curve is open downwards.
The equation of the form $(x-h)^2=4a(y-k)$
(ie) $(x-0)^2=-4\times 2(y-4)$
On simplifying we get,
$x^2+8y-32$ is the required equation of the parabola.